-3(2x-4)=3x(x-6)

Solution for -3(2x-4)=3x(x-6) equation:

-3(2x-4)=3x(x-6)

We move all terms to the left:

-3(2x-4)-(3x(x-6))=0

We multiply parentheses

-6x-(3x(x-6))+12=0


We calculate terms in parentheses: -(3x(x-6)), so:

3x(x-6)

We multiply parentheses

3x^2-18x

Back to the equation:

-(3x^2-18x)


We get rid of parentheses

-3x^2-6x+18x+12=0

We add all the numbers together, and all the variables

-3x^2+12x+12=0

a = -3; b = 12; c = +12;
Δ = b2-4ac
Δ = 122-4·(-3)·12
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*-3}=\frac{-12-12\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*-3}=\frac{-12+12\sqrt{2}}{-6}
$